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Distance and angles between Teichmüller geodesics

Lixin Liu Department of Mathematics, Sun Yat-sen University, 510275, Guangzhou Weixu Su Department of Mathematics, Fudan University, 200433, Shanghai, PR China Youliang Zhong School of Mathematics, South China University of Technology, 510641, Guangzhou, PR China

Complex Variables and Complex Analysis mathscidoc:2203.08008

Advances in Mathematics, 360, (22), 2020.1
We show that the angles between Teichmüller geodesic rays issuing from a common point, defined by using the law of cosines, do not always exist. The proof uses an estimation for the Teichmüller distance on finite dimensional Teichmüller spaces. As a consequence, the Teichmüller space equipped with the Teichmüller metric is not a CAT(k) space for any k∈R . We also discuss some necessary conditions for the existence of angle between the Teichmüller geodesics.
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@inproceedings{lixin2020distance,
  title={Distance and angles between Teichmüller geodesics},
  author={Lixin Liu, Weixu Su, and Youliang Zhong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220317150500018148988},
  booktitle={Advances in Mathematics},
  volume={360},
  number={22},
  year={2020},
}
Lixin Liu, Weixu Su, and Youliang Zhong. Distance and angles between Teichmüller geodesics. 2020. Vol. 360. In Advances in Mathematics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220317150500018148988.
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